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 A352603 a(1) = 2; a(2) = 3; for n >= 3, a(n) = a(n-1) - (gpf(n-2) + gpf(n-1)) if a(n) >= 2 and has not previously appeared, otherwise a(n) = a(n-1) + (gpf(n-2) + gpf(n-1)), where gpf(k) = A006530(k) = greatest prime dividing k. 1
 2, 3, 8, 13, 28, 48, 38, 16, 37, 76, 20, 44, 60, 76, 52, 84, 64, 55, 42, 24, 14, 4, 13, 28, 48, 58, 26, 68, 98, 74, 30, 72, 80, 88, 104, 128, 113, 228, 96, 118, 56, 122, 54, 118, 180, 116, 82, 12, 56, 46, 76, 34, 70, 94, 40, 92, 120, 148, 106, 196, 136, 112, 136, 160, 138, 110, 144, 130, 114 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This sequence uses a similar rule to the Recaman sequence A005132 except that here the step size is set to be the sum of the greatest primes dividing the previous two terms. In the first 100000 terms many small numbers do not appear, e.g., 5, 6, 7, 9. It is unknown if these eventually appear. In the same range numerous numbers appear multiple times, e.g., 47964 appears six times. The largest term in the range is a(98963) = 1529048. LINKS Scott R. Shannon, Line graph of the first 100000 terms. EXAMPLE a(3) = 8 as gpf(2) + gpf(3) = 2 + 3 = 5, so a(3) = a(2) + 5 = 8. a(4) = 13 as gpf(3) + gpf(8) = 3 + 2 = 5, and as 8 - 5 = 3 has already appeared, a(4) = a(3) + 5 = 13. a(7) = 38 as gpf(28) + gpf(48) = 7 + 3 = 10, and as 48 - 10 = 38 has not appeared, a(7) = 38. CROSSREFS Cf. A006530, A005132, A000040. Sequence in context: A116503 A291589 A105204 * A318621 A045692 A103196 Adjacent sequences:  A352600 A352601 A352602 * A352604 A352605 A352606 KEYWORD nonn AUTHOR Scott R. Shannon, Mar 22 2022 STATUS approved

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Last modified July 5 05:47 EDT 2022. Contains 355087 sequences. (Running on oeis4.)